(w+6)(w+6)+7=39

Solution for (w+6)(w+6)+7=39 equation:

Simplifying
(w + 6)(w + 6) + 7 = 39

Reorder the terms:
(6 + w)(w + 6) + 7 = 39

Reorder the terms:
(6 + w)(6 + w) + 7 = 39

Multiply (6 + w) * (6 + w)
(6(6 + w) + w(6 + w)) + 7 = 39
((6 * 6 + w * 6) + w(6 + w)) + 7 = 39
((36 + 6w) + w(6 + w)) + 7 = 39
(36 + 6w + (6 * w + w * w)) + 7 = 39
(36 + 6w + (6w + w2)) + 7 = 39

Combine like terms: 6w + 6w = 12w
(36 + 12w + w2) + 7 = 39

Reorder the terms:
36 + 7 + 12w + w2 = 39

Combine like terms: 36 + 7 = 43
43 + 12w + w2 = 39

Solving
43 + 12w + w2 = 39

Solving for variable 'w'.

Reorder the terms:
43 + -39 + 12w + w2 = 39 + -39

Combine like terms: 43 + -39 = 4
4 + 12w + w2 = 39 + -39

Combine like terms: 39 + -39 = 0
4 + 12w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 12w + -4 + w2 = 0 + -4

Reorder the terms:
4 + -4 + 12w + w2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 12w + w2 = 0 + -4
12w + w2 = 0 + -4

Combine like terms: 0 + -4 = -4
12w + w2 = -4

The w term is 12w.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12w + 36 + w2 = -4 + 36

Reorder the terms:
36 + 12w + w2 = -4 + 36

Combine like terms: -4 + 36 = 32
36 + 12w + w2 = 32

Factor a perfect square on the left side:
(w + 6)(w + 6) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(w + 6) equal to 5.656854249 and -5.656854249.

Subproblem 1
w + 6 = 5.656854249

Simplifying
w + 6 = 5.656854249

Reorder the terms:
6 + w = 5.656854249

Solving
6 + w = 5.656854249

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + w = 5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + w = 5.656854249 + -6
w = 5.656854249 + -6

Combine like terms: 5.656854249 + -6 = -0.343145751
w = -0.343145751

Simplifying
w = -0.343145751

Subproblem 2
w + 6 = -5.656854249

Simplifying
w + 6 = -5.656854249

Reorder the terms:
6 + w = -5.656854249

Solving
6 + w = -5.656854249

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + w = -5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + w = -5.656854249 + -6
w = -5.656854249 + -6

Combine like terms: -5.656854249 + -6 = -11.656854249
w = -11.656854249

Simplifying
w = -11.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.343145751, -11.656854249}